Liverpool fans do not care to be reminded that Nikica Jelavic cost Everton a seventh of the £35m Kenny Dalglish invested in Andy Carroll. The Croatia striker's five goals in 10 games since his January arrival from Rangers have transformed the fortunes of David Moyes's side and Slaven Bilic believes he could prove a key figure during Saturday's all-Merseyside FA Cup semi-final.

The Croatia coach and former Everton defender is from Split, where Jelavic began his career, and had long suspected that Goodison Park might prove his compatriot's ideal habitat. "I've known Nikica since he was a child and I watched Everton a lot, even before he came, and always imagined he'd suit them perfectly," said Bilic. "I've always been quite sure about Nikica.

"They needed a guy who is not only a finisher but is also great in other areas and they have found a natural goalscorer who is great in the buildup. He can hold the ball up, he's just perfect for Everton's style. You need a bit of luck at the start, which he got and now his confidence is sky high. He never panics, he's such a cool finisher. It doesn't surprise me how well he's doing."

What has startled Bilic is that Moyes was able to secure a 26-year-old known as the "Flying Fortress" in Croatia for such a relatively modest sum. "When I read about £20m transfers, getting him for £5m looks like a bargain," he said. "It's great for Everton."

Marrying match-winning quality with value for money proved an equation Damien Comolli, Liverpool's newly departed director of football, frequently struggled to balance but Moyes has long been adept at identifying sometimes slightly "left field" bargains. "It's not the first time Everton have done something like this," said Bilic. "They know the formula."

After coming close to recruiting Jelavic when the striker swapped Rapid Vienna for Rangers, Everton's manager monitored the 6ft 2in centre-forward's goals and burgeoning link-up play at Ibrox with acute interest. As time passed, Jelavic's elusive movement and cultured finishing – he frequently passes the ball into the net – reminded him increasingly of Davor Suker, Croatia's all-time top scorer. "I meet David Moyes at games and at the training ground but, although we speak about football, he didn't need to ask about Nikica," Bilic said.

Whereas Carroll's immaturity has slowed his progress following that record-breaking move from Newcastle in January 2011, Jelavic's personality appears ideally suited to coping with the leap involved in exchanging Scotland for the Premier League. "On one hand he's a model professional and so down to earth, that's how he's been brought up," says Bilic. "But on the other Nikica is so self-confident he never has any fear. I'm expecting him to improve even more – he has no limits. His best years are still to come; I think he can become one of the most important strikers in the league next season."

By then Bilic, who "misses" English football, and retains immense affection for Everton, might conceivably be at the helm of a Premier League club. "I've been in charge of the national team for six years and that will always be the proudest job I have," he says. "But I'm more of a club manager. I want to work every day."

First there is Euro 2012 to challenge for and, more immediately, a potentially campaign-defining FA Cup semi-final to watch. "The season wasn't good for Everton until a couple of months ago," says the 43-year-old. "But now it looks like it could be a great one. Full respect to David Moyes."

Should his side overcome Liverpool before winning next month's final, Everton's manager may prefer to delegate considerable credit to the quiet, low key, £5m striker he has dubbed "our silent assassin."